Download Vocabulary: Prime Time Concept Example Factor: A whole number

Vocabulary: Prime Time
Concept
Factor: A whole number that divides into another
whole number evenly (that is, with no remainder and
a whole number quotient).
Example
4 is a factor of 24 because 4 x ? = 24 leads
to the conclusion that the other factor is the
whole number 6. We can use the term
divisor interchangeably with factor.
Factor Pair: A pair of factors that can be multiplied to 2 and 12 are a factor pair for 24, as are 3
make a target number.
and 8.
Multiple: A whole number that can be divided by a
given whole number factor.
24 is a multiple of 8, because 8 is a factor
of 24.
Prime Number: A prime number has factors of only
1 and itself. (1 and 0 are not primes.)
Composite Number: A number with factors other
than 1 and itself.
19 is a prime because the only factors are
1 and 19, but 9 is not a prime because it
has factors 1, 3, 9.
14 is a composite number because 14 has
factors 2 and 7, as well as 1 and 14.
Prime Factorization: A prime factorization of a
number is the list of prime numbers that would
multiply together to make the given number.
The prime factorization of 24 is 2 x 2 x 2 x
3, where all of the factors are prime. It is
true that 24 = 3 x 8 or 2 x 4 x 3 or 6 x 2 x 2
etc. But, these last three factorizations are
not prime factorizations, because “8” and
“4” and “6” are not prime numbers. See
below for an example of finding a prime
factorization of 40.
Fundamental Theorem of Arithmetic: This
theorem says that the prime factorization of any
number is unique.
If we start with 40 and think of this as 2 x
20, then we should “break down” 20
further, since it is not prime. Thus, 40 = 2
x 20 = 2 x 2 x 10 = 2 x 2 x 2 x 5. This is a
prime factorization of 40. If we started with
a different factor pair, say 40 = 5 x 8, and
then “broke down” 8 further, we would get
40 = 5 x 8 = 5 x 2 x 2 x 2. The resulting
prime factorization of 40 is the same
(except for order) no matter how we begin
on the process.
Greatest Common Factor: A common factor is any
number that is a factor that 2 or more whole
numbers. One way to find common factors is to
make prime factorizations of the two numbers in
question.
36 = 2 x 2 x 3 x 3 and 84 = 2 x 2 x 3 x 7.
We see that the factors 2, 2 and 3 appear
in both prime factorizations; so 2, 3, 6
(combining 2 and 3), 4 (combining 2 and 2)
and 12 (combining 2 and 2 and 3) are
common factors of both 36 and 84. 12 is
the greatest of these so 12 is the GCF.
Lowest Common Multiple: The LCM is the lowest
whole number that is a multiple of 2 or more whole
numbers. One way to find the LCM is to make prime
factorizations of the target numbers.
36 = 2 x 2 x 3 x 3 and 84 = 2 x 2 x 3 x 7.
We need the lowest combination of prime
factors that will include ALL of the prime
factors for each of these numbers. If we
start with 2 x 2 x 3 x 3 (to “cover” 36) then
we see that we need to extend this to 2 x 2
x 3 x 3 x 7 (to “cover” 84). So 2 x 2 x 3 x 3
x 7 or 252 is the lowest whole number that
is a multiple of both 36 and 84.
Relatively Prime: Two numbers are relatively prime 25 and 21 are relatively prime because 25
if they have no prime factors in common other than 1. = 5 x 5 and 21 = 3 x 7, so there are no
prime factors in common. 25 and 30 are
not relatively prime because 25 = 5 x 5 and
30 = 2 x 3 x 5, so they have a “5” in
common. 26 and 13 are not relatively
prime because they each have 13 as a
factor.
Rectangular Array: One way of modeling
multiplication of factor pairs is to picture these as the
dimensions of a rectangle.
12 can be thought of as 2 x 6 (2 rows of 6)
or 3 x 4 or 1 x 12.
Venn Diagram: A visual way of organizing
information logically to show what is included or
excluded from a definition.
See Prime Time Homework Examples
from ACE on this website.
(Investigation 2 #17)